761 research outputs found
On the reachability and observability of path and cycle graphs
In this paper we investigate the reachability and observability properties of
a network system, running a Laplacian based average consensus algorithm, when
the communication graph is a path or a cycle. More in detail, we provide
necessary and sufficient conditions, based on simple algebraic rules from
number theory, to characterize all and only the nodes from which the network
system is reachable (respectively observable). Interesting immediate
corollaries of our results are: (i) a path graph is reachable (observable) from
any single node if and only if the number of nodes of the graph is a power of
two, , and (ii) a cycle is reachable (observable) from
any pair of nodes if and only if is a prime number. For any set of control
(observation) nodes, we provide a closed form expression for the (unreachable)
unobservable eigenvalues and for the eigenvectors of the (unreachable)
unobservable subsystem
Controllability of multi-agent systems with input and communication delays
Distributed cooperative control of multi-agent systems is broadly applied in artificial intelligence in which time delay is of great concern because of its ubiquitous. This paper considers the controllability of leader-follower multi-agent systems with input and communication delays. For the first-order systems with input delay, neighbor-based protocol is adopted to realize the interactions among agents, yielding a system with delay existed in state and control input. New notions of interval controllability and interval structural controllability for the system are defined. Algebraic criterion is established for interval controllability, and graph-theoretic interpretation is put forward for the interval structural controllability. Results imply that input delay of the multi-agent systems has significant influence on the interval controllability and interval structural controllability. Corresponding conclusions are generalized to the first-order systems and the high-order ones with communication delays, respectively. Example is attached to illustrate the work
Controllability and observability of grid graphs via reduction and symmetries
In this paper we investigate the controllability and observability properties
of a family of linear dynamical systems, whose structure is induced by the
Laplacian of a grid graph. This analysis is motivated by several applications
in network control and estimation, quantum computation and discretization of
partial differential equations. Specifically, we characterize the structure of
the grid eigenvectors by means of suitable decompositions of the graph. For
each eigenvalue, based on its multiplicity and on suitable symmetries of the
corresponding eigenvectors, we provide necessary and sufficient conditions to
characterize all and only the nodes from which the induced dynamical system is
controllable (observable). We discuss the proposed criteria and show, through
suitable examples, how such criteria reduce the complexity of the
controllability (respectively observability) analysis of the grid
- …